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This lecture covers the basics of topic models, starting with clustering and density estimation, then delving into Gaussian Mixture Models (GMM) and the Latent Dirichlet Allocation (LDA) model. The instructor explains the algorithms, learning processes, and limitations of GMM and LDA, as well as the concepts of Dirichlet distribution and variational inference. The lecture concludes with extensions to the LDA model and the application of variational inference to Gaussian Mixture Models.